Generalized Farey trees, transfer Operators and phase transitions

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral analysis of generalized transfer operators. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.Comment: 39 pages, 10 figure

Use of Z-pinch radiation sources for high-pressure shock wave studies

The authors are developing a new shock wave diagnostic using Z pinch sources for high-pressure equation of state (EOS) measurements. Specifically, they are employing VISAR interferometry to measure the particle velocity of shocked materials and fiber optic probes to measure the shock speed. Combination of these measurements will allow absolute EOS data with Z accelerators. This report is a progress report on the development of this new approach to EOS measurements; however, preliminary data obtained with the diagnostics are encouraging. With further development of Z pinch sources, it is envisioned that a variety of EOS and constitutive property measurements can be made. Time-resolved wave profile measurements will then provide a variety of EOS and material property data, such as isentropic EOS, initial compressive strength and shock-induced compressive strength, dynamic tensile strength, kinetics of phase transitions, and surface stability studies

The "Z" Pulsed Radiation Source: Recent Developments in Equation of State Measurement Capabilities

The Sandia Z machine is a source of intense radiation which can be used to drive ablative shocks for equation of state studies. In developing the capability to diagnose these types of studies on Z, techniques commonly used in conventional impact generated experiments were leveraged. The primary diagnostic transferred was velocity interferome~, VLSAR, [1] which not only provides Hugoniot particle velocity measurements, but also indications of shock stability and wave attenuation. In addition to a VISAR capability on the Z machine, methods for measuring shock velocity have been developed. When these measured parameters are used in conjunction with the Rankine-Hugoniot jump conditions, [2] material response at high temperatures and pressures can be inferred. With sample sizes used on Z being much smaller than those fielded in typical impact experiments, temporal resolution and methods of interfacing the diagnostics with the targets had to be improved. In this paper, a "standard" equation of state experiment, associated diagnostics, and some recent results in aluminum and beryllium will be discussed

Sandia National Laboratories shock thermodynamics applied research (STAR) facility

The Sandia National Laboratories Shock Thermodynamics Applied Research (STAR) Facility has recently consolidated three different guns and a variety of instrumentation capabilities into a single location. The guns available at the facility consist of a single-stage light gas gun, a single-stage propellant gun and a two-stage light gas gun, which cover a velocity range from 15 m/s to 8 km/s. Instrumentation available at the facility includes optical and microwave interferometry, time-resolved holography, fast x-radiography, framing and streak photography, fast multi-wavelength pyrometry, piezoelectric and piezoresistive gauges and computer data reduction. This report discusses the guns and instrumentation available at the facility and selected recent applications

Isentropic Compression Experiments on the Z Accelerator

This paper provides a brief review of experimental techniques for producing dynamic isentropic compression of samples to pressures of several hundred GPa. Traditional gun launch techniques include use of buffer plates, such as fused silica, that exhibit negative curvature to their stress-strain response and graded-density impactors. Graded-density impactors have been used to study isentropic compression of specimens to pressures exceeding 2 Mbar on high-impedance materials. A recent development includes the use of the Sandia Z Accelerator to produce magnetic compression in planar specimens to pressures of a few hundred kbar over time scales of 100 ns. These techniques have been successfully applied to isentropic compression of iron to 300 kbar and copper to 130 kbar. The iron results indicate that it is possible to study the polymorphic phase change that occurs at 130 kbar and also the kinetic properties of the transformation. The copper results indicate that with further improvements in progress it should be possible to measure continuous isentropic compression curves in materials of interest to pressures exceeding 1 Mbar. The Z accelerator is limited to peak currents of about 20 MA. By reconfiguring the anode-cathode geometry it should be possible to obtain constant current density and thus driving pressure to about 3 Mbar. The next generation accelerator referred to as ZX, which is being proposed will have the capability to generate currents to 50 MA and resulting peak pressures to 15 Mbar

Effect of shock wave risetime on material ejection from aluminum surfaces

The effect of shock wave risetime on material ejection in aluminum has been studied for loading stresses of 21 GPa. Uniform loading was accomplished with plate impact techniques by mounting specimens on a ramp wave generator. Projectile impact on one side of the wave generator produced a wave which dispersed with propagation distance. This wave was then made incident to an aluminum specimen, so that the specimen experienced non-shock loading. It was found that mass ejection from aluminum surfaces can be reduced by over two orders of magnitude relative to shock loading conditions by accelerating the surface with a wave risetime greater than about 35 ns. These results suggest an explanation for the apparent discrepancies which are sometimes observed in mass ejection measurements utilizing either plate impact or electron beam deposition to generate stress waves

Use of Z-pinch sources for high-pressure shock wave studies

In this paper, we will discuss the use of z-pinch sources for shock wave studies at multi-Mbar pressures. Experimental plans to use the technique for absolute shock Hugoniot measurements are discussed. Recent developments have demonstrated the use of pulsed power techniques for producing intense radiation sources (Z pinches) for driving planar shock waves in samples with spatial dimensions significantly larger than possible with other radiation sources. Initial indications are that using Z pinch sources for producing Planckian radiation sources in secondary hohlraums can be used to drive shock waves in samples with diameters to a few millimeters and thickness approaching one millimeter in thickness. These dimensions provides the opportunity to measure both shock velocity and the particle velocity behind the shock front with accuracy comparable to that obtained with gun launchers. In addition, the peak hohlraum temperatures of nearly 150 eV that are now possible with Z pinch sources result in shock wave pressures approaching 45 Mbar in high impedance materials such as tungsten and 10-15 Mbar in low impedance materials such as aluminum and plastics. In this paper, we discuss the use of Z pinch sources for making accurate absolute EOS measurements in the megabar pressure range

Z-Pinch Driven Isentropic Compression for Inertial Fusion

The achievement of high gain with inertial fusion requires the compression of hydrogen isotopes to high density and temperatures. High densities can be achieved most efficiently by isentropic compression. This requires relatively slow pressure pulses on the order of 10-20 nanoseconds; however, the pressure profile must have the appropriate time. We present 1-D numerical simulations that indicate such a pressure profile can be generated by using pulsed power driven z pinches. Although high compression is calculated, the initial temperature is too low for ignition. Ignition could be achieved by heating a small portion of this compressed fuel with a short (-10 ps) high power laser pulse as previously described. Our 1-D calculations indicate that the existing Z-accelerator could provide the driving current (-20 MA) necessary to compress fuel to roughly 1500 times solid density. At this density the required laser energy is approximately 10 kJ. Multidimensional effects such as the Rayleigh-Taylor were not addressed in this brief numerical study. These effects will undoubtedly lower fuel compression for a given chive current. Therefore it is necessary to perform z-pinch driven compression experiments. Finally, we present preliminary experimental data from the Z-accelerator indicating that current can be efficiently delivered to appropriately small loads (- 5 mm radius) and that VISAR can be used measure high pressure during isentropic compression